This applies mostly to rifles with wood stocks that might be used for multi-seasons/climate conditions.
First thing I look at after buying a rifle, especially a bolt-action, is the forend/barrel situation. If the barrel is bedded tightly against the barrel, especially if a wood stock, it's often going to change the point of impact with seasonal humidity changes and sling pressure (if used to shoot). If the barrel is touching wood on only one side, it's usually going to cause diagonal stringing of shots. It's also likely to cause larger grouping of shots.
It's relatively easy to sand, rasp, or otherwise open the barrel channel so the barrel is a uniform 1/16" or so away from the wood or synthetic forend. Synthetic stocks won't change clearance with seasonal weather/temperature changes, but are often quite flexible, so if you plan to use a tight sling to help your shots, consider more clearance, so the barrel can vibrate on it's own and not affected by sling tension, or resting the forend on various materials, especially hard ones, to shoot at sighting-in targets. Diagonal stringing of groups is often caused by poor barrel-forend bedding.
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While the rifle is apart, check the action to see if it is tight to it's bedding, or whether the action can move around a lot when the screws are out and it's still sitting on it's cradle. Seemingly loose fit of the action/bedding might be easily improved by epoxy bedding, but that's another topic.
First thing I look at after buying a rifle, especially a bolt-action, is the forend/barrel situation. If the barrel is bedded tightly against the barrel, especially if a wood stock, it's often going to change the point of impact with seasonal humidity changes and sling pressure (if used to shoot). If the barrel is touching wood on only one side, it's usually going to cause diagonal stringing of shots. It's also likely to cause larger grouping of shots.
It's relatively easy to sand, rasp, or otherwise open the barrel channel so the barrel is a uniform 1/16" or so away from the wood or synthetic forend. Synthetic stocks won't change clearance with seasonal weather/temperature changes, but are often quite flexible, so if you plan to use a tight sling to help your shots, consider more clearance, so the barrel can vibrate on it's own and not affected by sling tension, or resting the forend on various materials, especially hard ones, to shoot at sighting-in targets. Diagonal stringing of groups is often caused by poor barrel-forend bedding.
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While the rifle is apart, check the action to see if it is tight to it's bedding, or whether the action can move around a lot when the screws are out and it's still sitting on it's cradle. Seemingly loose fit of the action/bedding might be easily improved by epoxy bedding, but that's another topic.